Related papers: On the Yang-Baxter equation for the six-vertex mod…
In this work we relate the spectral problem of the toroidal six-vertex model's transfer matrix with the theory of integrable non-linear differential equations. More precisely, we establish an analogy between the Classical Inverse Scattering…
The spectral decomposition of regular sl_2-invariant R-matrices R(lambda) is studied by means of the method of reduction of the Yang-Baxter equation onto subspaces of a given spin. Restrictions on the possible structure of several highest…
Let $A$ be a $2\times 2$ matrix over a finite field and consider the Yang-Baxter matrix equation $XAX=AXA$ with respect to $A$. We use a method of computational ideal theory to explore the geometric structure of the affine variety of all…
We consider a general class of boundary terms of the open XYZ spin-1/2 chain compatible with integrability. We have obtained the general elliptic solution of $K$-matrix obeying the boundary Yang-Baxter equation using the $R$-matrix of the…
We study all five-, six-, and one eight-vertex type two-state solutions of the Yang-Baxter equations in the form $A_{12} B_{13} C_{23} = C_{23} B_{13} A_{12}$, and analyze the interplay of the `gauge' and `inversion' symmetries of these…
We suggest the elliptic $16\times16$ R-matrix for the XX spin chain in a staggered magnetic field. This integrable model is a special case of the more general one, studied long ago within the alternative approach by V. M. Kontorovich and V.…
This paper considers aspects of a Kagome lattice system with states classified by plane partitions. Using two sets of free fermions, we rewrite the lattice in terms of two families of spin chains. In this formalism, the quantum crystals…
It is shown that for a certain class of Yang-Baxter maps (or set-theoretical solutions to the quantum Yang-Baxter equation) the Lax representation can be derived straight from the map itself. A similar phenomenon for 3D consistent equations…
We introduce a class of new integrable lattice models labeled by a pair of positive integers N and r. The integrable model is obtained from the Gauge/YBE correspondence, which states the equivalence of the 4d N=1 S^1 \times S^3/Z_r index of…
We study Yang-Baxter deformations of the flat space string that result in exactly solvable models, finding the Nappi-Witten model and its higher dimensional generalizations. We then consider the spectra of these models obtained by canonical…
This paper aims to introduce a construction technique of set-theoretic solutions of the Yang-Baxter equation, called strong semilattice of solutions. This technique, inspired by the strong semilattice of semigroups, allows one to obtain new…
In this paper we derive from arguments of string scattering a set of eight tetrahedron equations, with different index orderings. It is argued that this system of equations is the proper system that represents integrable structures in three…
Inspired by the integrable structures appearing in weakly coupled planar N=4 super Yang-Mills theory, we study Q-operators and Yangian invariants of rational integrable spin chains. We review the quantum inverse scattering method along with…
Functional equations methods are a fundamental part of the theory of Exactly Solvable Models in Statistical Mechanics and they are intimately connected with Baxter's concept of commuting transfer matrices. This concept has culminated in the…
We show that the celebrated six-vertex model of statistical mechanics (along with its multistate generalizations) can be reformulated as an Ising-type model with only a two-spin interaction. Such a reformulation unravels remarkable…
We develop an approach for constructing the Baxter Q-operators for generic sl(N) spin chains. The key element of our approach is the possibility to represent a solution of the the Yang Baxter equation in the factorized form. We prove that…
We study the general solution of the Yang-Baxter equation with deformed $sl(2)$ symmetry. The universal R operator acting on tensor products of arbitrary representations is obtained in spectral decomposition and in integral forms. The…
We develop Yang-Baxter integrability structures connected with the quantum affine superalgebra Uq(\hat sl(2|1)). Baxter's Q-operators are explicitly constructed as supertraces of certain monodromy matrices associated with (q-deformed)…
Starting with any R-matrix with spectral parameter, obeying the Yang-Baxter equation and a unitarity condition, we construct the corresponding infinite dimensional quantum group U_{R} in term of a deformed oscillators algebra A_R. The…
We introduce new methods to describe admissible states of the six-vertex and the eight-vertex lattice models of statistical mechanics. For the six-vertex model, we view the admissible states as differential forms on a grid graph. This…